tentia integra n 9 A n x 11 == 1, 2. 3. . . n quantitas conftans. 

 Q. E. D. 



$„ 4. Hinc iimul patet, A n ~~ T x n pro quavis poten- 

 tia integra n effe progreffionem Arithmeticam , cuius diffe- 

 rentia A n x n — 1. 2. 3« • • rc. 



Si Xn.flx", facile perfpicitur, effe 

 A n X ~ a. 1. 2. 3. . . 72. 

 Eft nempe 



A X =z a (x -f- i) n — a x n z= a . A x n 9 



'A X — a {x -h 2f — a (x -\- i) n ~ a.'A x n , 

 ideoque 



A^X—^AX — AX — aCAx n — Ax n )~a. A 2 x\ 

 Quare curn quaelibet difFereniia luperior A n-f-1 per inferio- 

 zes A n , A n ~" % -, etc. aequationibus finiplicibus detur (§. 3.), 

 fequitur A n . a x n ~ a . A n x' L ~ a. 1 2. 3. . . «. 



^. 5. Propolita iam fun&ione integra 



Ax^ + Bx^ 1 ^ . . , . = X, 



euius fa&or fit 



a x 1 ■-+- b x n ~ x -h- cx"" 2 + ,. . .~hfxx^-gx~hh~y, 



ita ut fit X=jY, exiftente Y produfto fa&orum k x* ■+■ 

 Ix' t_I + . . . et p x* -+■ c/ x 71- ~ l -+- . .., erit functionis X ter- 

 minus fupiemus aequalis produ&o terminorum fummorum 

 omnium fa&omm, h. e. A x m — a x n k x K p x 71 ", five w=:n + 

 X-+-7T, et A — akp, proinde eit a faclor Coefficientis A. 

 Si iam variabili x fucceffive valores tribuantur progredien- 

 tes ferie Arithmetica, cuius diffeientia ~ 1, valorque re- 

 Nova AUa Acad. Imp. Sclent. Jom. XI. Z fpon- 



S 



